Abstract
We extend the biquaternionic Dirac equation to include interactions with a background bosonic Geld. The obtained biquaternionic Dirac equation yields Maxwell-like equations that hold for both a matter Geld and an electromagnetic Geld. We establish that the electric Geld is perpendicular to the matter magnetic Geld and the magnetic Geld is perpendicular to the matter inertial Geld. We show that the inertial and magnetic masses are conserved separately. The magnetic mass density arises as a result of the coupling between the vector potential and the matter inertial Geld. The presence of the vector and scalar potentials and also the matter inertial and magnetic Gelds modify the Standard form of the derived Maxwell equations. The resulting interacting electrodynamics equations are generalizations of the equations of Wilczek or Chern-Simons axion-like Gelds. The coupled Geld in the biquaternioic Dirac Geld reconstructs the Wilczek axion Geld. We show that the electromagnetic Geld vector \(\overrightarrow{F}=\overrightarrow{E}+ic\overrightarrow{B}\), where \(\overrightarrow{E}\) and \(\overrightarrow{B}\) are the respective electric and magnetic Gelds, satisGes the massive Dirac equation and, moreover, \(\overrightarrow{\triangledown}\cdot\overrightarrow{F}=0\).
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Prepared from an English manuscript submitted by the author; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 203, No. 2, pp. 231–250, May, 2020.
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Arbab, A.I. Coupling of a biquaternionic Dirac field to a bosonic field. Theor Math Phys 203, 631–647 (2020). https://doi.org/10.1134/S0040577920050062
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DOI: https://doi.org/10.1134/S0040577920050062